The 7 nodes of the Fano plane — the combinatorial geometry underlying octo- nion multiplication — map exactly onto 7 orbital quantum dot (QD) modes in the Transdimensional Anomalous Hall Effect (TDAHE) ground state of rhombohedral graphene. The adjacency graph of the Fano plane is the complete graph K7: every QD couples to all 6 others, with the coupling sign and mediation structure deter- mined by the unique Fano line through each pair. The ternary gate F({i, j}) = |k⟩ (output is the unique third node on the Fano line through i and j) gives a complete 7-gate primitive set closed under G2. We prove that the Fano-Toffoli associator FT(i, j, k) = [(eiej)ek] −[ei(ejek)] is zero if and only if (i, j, k) lies on a Fano line — precision 1.000, recall 1.000, confirmed exhaustively over all 210 ordered triples. This makes FT a perfect hardware error detector: TDAHE ground states are Fano- line correlated (FT = 0 always); any perturbation exits the Fano line (FT ̸= 0 immediately). The chiral Bell measurement uses ABC/CBA-stacked interferometer pairs; fidelity per 3-step teleportation protocol is (1 −fbulk)3 = 89.3% from pion kinematics alone, versus 82±1% for Laneve et al. (2025) using engineered dissimilar quantum dots. ContentsPart of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.